Linear Restriction Estimates for Schrödinger Equation on Metric Cones

Junyong Zhang*

*此作品的通讯作者

科研成果: 期刊稿件文章同行评审

7 引用 (Scopus)

摘要

In this paper, we study some modified linear restriction estimates of the dynamics generated by Schrödinger operator on metric cone M, where the metric cone M is of the form M = (0, ∞)r × Σ, with the cross section Σ being a compact (n − 1)-dimensional Riemannian manifold (Σ, h) and the equipped metric being g = dr2 + r2h. Assuming the initial data possesses additional regularity in angular variable θ ∈ Σ, we show some linear restriction estimates for the solutions. In terms of their applications, we obtain global-in-time Strichartz estimates for radial initial data and show small initial data scattering theory for the mass-critical nonlinear Schrödinger equation on two-dimensional metric cones.

源语言英语
页(从-至)995-1028
页数34
期刊Communications in Partial Differential Equations
40
6
DOI
出版状态已出版 - 3 6月 2015

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